MissDDIM: Deterministic Diffusion for Tabular Imputation

• MissDDIM is a conditional diffusion framework for tabular data imputation that uses deterministic DDIM sampling to infer missing values based on observed entries.
• It replaces the slow, variable stochastic DDPM sampling with a streamlined deterministic reverse process, significantly reducing inference latency and output variability.
• Empirical results show that MissDDIM achieves competitive RMSE and runtime improvements on benchmark datasets while providing reproducible, single-pass imputations.

Searching arXiv for MissDDIM and closely related DDIM/imputation work to ground the article in current papers. MissDDIM is a conditional diffusion framework for tabular data imputation that adapts Denoising Diffusion Implicit Models (DDIM) to generate missing values conditioned on observed values. Its central design choice is to replace the stochastic, many-step DDPM sampling procedure used by prior diffusion imputers with a DDIM-style deterministic sampling path, with the stated aim of reducing inference latency and output variability while preserving the generative formulation of conditional imputation (Zhou et al., 5 Aug 2025).

1. Problem setting and methodological motivation

MissDDIM addresses conditional generation over partially observed rows of a table. The task is to infer missing features from observed features within a row, rather than to generate entire samples unconditionally. The paper frames the objective as modeling the conditional distribution of the missing part given the observed part of a tabular record, with diffusion applied only to the target subset and the observed subset used as conditioning context (Zhou et al., 5 Aug 2025).

The motivation is explicitly operational. Prior diffusion imputers for tabular data are described as typically relying on stochastic DDPM sampling, which introduces three practical difficulties. First, inference is slow because sampling proceeds sequentially over many timesteps. Second, outputs vary across runs, which complicates pipelines that require stable single imputations. Third, some prior approaches assume fully observed training data or do not natively exploit partially observed rows during training. In the experimental protocol summarized in the paper, diffusion baselines use $T=100$ steps and 100 stochastic samples per instance with median aggregation to stabilize outputs, and this is presented as a major source of inference cost (Zhou et al., 5 Aug 2025).

Within the broader diffusion literature, MissDDIM inherits the DDIM premise that a model trained with DDPM-style noise prediction need not be sampled through a fully stochastic reverse chain. DDIM introduced deterministic or partially stochastic non-Markovian reverse trajectories that preserve the standard diffusion training procedure while enabling much faster sampling (Song et al., 2020). MissDDIM specializes that idea to missing-data imputation in static tabular settings.

2. Conditional diffusion formulation for tabular imputation

The paper begins from the standard DDPM forward process. If $\mathbf{x}_0 \sim q(\mathbf{x}_0)$, Gaussian noise is added over $T$ steps through

$$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$

which induces the closed-form marginal

$$q(\mathbf{x}_t \mid \mathbf{x}_0) = \mathcal{N}(\mathbf{x}_t; \sqrt{\alpha_t}\mathbf{x}_0,\ (1-\alpha_t)\mathbf{I}), \quad \alpha_t = \prod_{i=1}^t (1-\beta_i).$$

The reverse process is parameterized as a Gaussian transition with a noise-prediction network $\epsilon_\theta$ defining the mean (Zhou et al., 5 Aug 2025).

MissDDIM modifies this setup in a conditional manner. Diffusion is applied only to the missing components, while observed components are treated as fixed conditioning variables. The reverse process therefore factorizes over the missing coordinates conditioned on the observed ones, and the denoising network is written as a conditional noise predictor that receives the noised missing entries, the timestep, and the observed entries of the same row (Zhou et al., 5 Aug 2025).

Training follows the standard DDPM/DDIM noise-prediction objective, specialized to the missing subset. Only the target or missing components are noised: $$\mathbf{x}_t^{\text{mis}} = \sqrt{\alpha_t}\,\mathbf{x}_0^{\text{mis}} + \sqrt{1-\alpha_t}\,\boldsymbol{\epsilon}, \qquad \boldsymbol{\epsilon}\sim\mathcal{N}(\mathbf{0},\mathbf{I}).$$ The network is trained to predict $\boldsymbol{\epsilon}$ from the noised missing entries, the timestep, and the observed conditioning variables, with objective

$$\min_\theta \mathcal{L}(\theta) = \mathbb{E}_{\mathbf{x}_0,\boldsymbol{\epsilon},t} \left[ \left\| \boldsymbol{\epsilon} - \epsilon_\theta(\mathbf{x}_t^{\text{mis}}, t \mid \mathbf{x}_0^{\text{obs}}) \right\|_2^2 \right],$$

where $t\sim\mathrm{Unif}(\{1,\dots,T\})$. This is presented as conditional denoising score matching rather than a new loss family (Zhou et al., 5 Aug 2025).

3. Deterministic DDIM trajectory and inference behavior

The main novelty of MissDDIM lies in inference rather than training. The paper states that DDIM introduces a non-Markovian reverse trajectory in which stochasticity is controlled by $\mathbf{x}_0 \sim q(\mathbf{x}_0)$0 or, equivalently in common notation, $\mathbf{x}_0 \sim q(\mathbf{x}_0)$1. MissDDIM adopts the deterministic setting by explicitly setting $\mathbf{x}_0 \sim q(\mathbf{x}_0)$2 for all $\mathbf{x}_0 \sim q(\mathbf{x}_0)$3, thereby removing sampling randomness and making the imputation trajectory deterministic once the input row is fixed (Zhou et al., 5 Aug 2025).

Operationally, the reverse process updates only the missing subset. The observed values are never generated and remain fixed throughout inference. At test time, the missing coordinates are initialized at the terminal noise level, the observed coordinates are kept unchanged, and the model repeatedly applies the conditional deterministic DDIM update until reaching $\mathbf{x}_0 \sim q(\mathbf{x}_0)$4. The final imputed row is then formed by combining the untouched observed entries with the final denoised missing entries. The paper does not present an explicit projection equation using a binary mask after every step, but it explicitly characterizes the mechanism as “freeze observed / denoise missing” conditioning (Zhou et al., 5 Aug 2025).

The practical consequence is reproducibility. The paper describes MissDDIM as producing a deterministic imputation from a single trajectory; it even uses the phrase “a single forward pass,” followed by the clarification that, more precisely, it is a single deterministic reverse trajectory through the selected timesteps. Because DDIM allows sub-sampling of the trajectory, MissDDIM can also use fewer reverse steps than the original training length (Zhou et al., 5 Aug 2025).

An ablation over $\mathbf{x}_0 \sim q(\mathbf{x}_0)$5 further sharpens the deterministic-stochastic trade-off. The qualitative finding is that $\mathbf{x}_0 \sim q(\mathbf{x}_0)$6 yields deterministic outputs with low variance, while larger $\mathbf{x}_0 \sim q(\mathbf{x}_0)$7 can sometimes slightly improve average error at high $\mathbf{x}_0 \sim q(\mathbf{x}_0)$8 but increases variability. Under 50% missingness, the average RMSE at $\mathbf{x}_0 \sim q(\mathbf{x}_0)$9 is reported as 0.4977 for $T$0, versus 0.7412 and 0.8170 for noisier settings; at $T$1, the average RMSEs are 0.3293 for $T$2, 0.3167 for $T$3, and 0.3343 for $T$4 (Zhou et al., 5 Aug 2025).

4. Training on incomplete data and architectural realization

A second practical contribution is the self-masking strategy used during training. Real tabular datasets often do not contain fully observed rows, so MissDDIM learns directly from incomplete data by randomly masking a subset of currently observed entries and treating them as pseudo-missing targets, while the remaining observed entries serve as conditioning context. In effect, each partially observed row becomes a supervised conditional denoising example. The paper emphasizes that this allows training without complete cases and without auxiliary imputations such as mean filling (Zhou et al., 5 Aug 2025).

Architecturally, the implementation is based on TabCSDI. The authors state that they adapt TabCSDI for non-sequential tabular data by removing the temporal transformer module, which was originally designed for time series, while retaining the feature-wise transformer encoder and residual MLP blocks. The contribution is described as sampler-level and model-agnostic in the sense that any DDPM-style imputer with a learned $T$5 could in principle use the DDIM sampler, although the reported implementation uses the TabCSDI-derived backbone (Zhou et al., 5 Aug 2025).

The training details remain relatively sparse. The loss is the $T$6 noise-prediction loss, timesteps are sampled uniformly, and the method uses the usual forward diffusion schedule with $T$7 and $T$8. Continuous features are standardized before imputation. Missing values in experiments are simulated at rates $T$9, $$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$0, $$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$1, and $$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$2. The description and figure caption indicate that the main evaluation is under simulated MCAR-style missingness, and the conclusion notes future work on “more complex missing data mechanisms,” which suggests a limited treatment of MAR and MNAR in the current study (Zhou et al., 5 Aug 2025).

5. Empirical performance, runtime, and downstream behavior

The empirical case for MissDDIM is built around two properties: lower inference cost and stable point imputation. In the runtime comparison, the diffusion baselines use 100 stochastic samples per instance with median aggregation, whereas MissDDIM produces a single deterministic output. At equal nominal $$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$3, MissDDIM is reported as competitive or better in RMSE while avoiding repeated sampling. When the number of DDIM steps is reduced to 50 or 20, runtime drops substantially, with only modest degradation in RMSE (Zhou et al., 5 Aug 2025).

Method	Time (s)	RMSE
CSDI	820.73	0.3730
TabCSDI	794.21	0.3319
MissDiff	765.92	0.3163
MissDDIM ($$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$4)	775.31	0.3051
MissDDIM ($$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$5)	385.12	0.3167
MissDDIM ($$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$6)	154.61	0.3343

The paper also reports strong downstream-task performance across five benchmark datasets: Adult, Banknote, California, Letter, and Student. These include continuous-only datasets and mixed-type datasets. Metrics are weighted F1 for classification and MAE for Student regression. MissDDIM is described as competitive with or best among all compared methods in many settings. Examples given in the text include 0.7228 F1 on Adult at 30% missingness, slightly above TabCSDI’s 0.7214; best performance on California at all three reported missing rates; best performance on Letter at all three reported rates; and the best MAE on Student at 30% and 50%, with second-best at 70% missingness. The RMSE figure and aggregated boxplots are also said to show superior stability across datasets and missingness levels (Zhou et al., 5 Aug 2025).

These results support the paper’s central interpretation of deterministic DDIM as a favorable stability-accuracy-speed compromise for tabular imputation. A plausible implication is that MissDDIM is most attractive when a single reproducible completion is operationally preferable to a stochastic ensemble.

6. Position within the DDIM literature, extensions, and limitations

MissDDIM is a DDIM adaptation for missing-data imputation, not an image-generation sampler. This distinction matters because several DDIM-family papers modify sampling in other directions. The original DDIM work defined the deterministic non-Markovian reverse process that MissDDIM relies on (Song et al., 2020). By contrast, “Improved DDIM Sampling with Moment Matching Gaussian Mixtures” replaces the standard DDIM single-Gaussian reverse transition with a moment-matching Gaussian mixture kernel to improve few-step image sampling, especially around 10-step sampling, but it is explicitly not called MissDDIM (Gabbur, 2023). Likewise, Denoising Diffusion Step-aware Models reduce per-step model cost by allocating different-width subnetworks across timesteps and are described as compatible with DDIM trajectories, but they address compute allocation rather than conditional missing-data reconstruction (Yang et al., 2023).

Within tabular imputation, the closest lineage is MissHDD, which explicitly positions itself as an extension of the earlier MissDDIM idea to heterogeneous incomplete data. MissHDD retains a continuous DDIM-based deterministic channel for numerical variables while adding a separate discrete diffusion channel for categorical and discrete variables. The paper’s own framing is that MissDDIM handled deterministic DDIM-based imputation for tabular data through a single diffusion process, whereas MissHDD separates continuous and discrete feature types into complementary channels (Zhou et al., 18 Nov 2025).

The limitations of MissDDIM are also explicit. The paper does not provide a deep treatment of heterogeneous feature modeling, and although it evaluates on mixed-type datasets, it does not fully specify categorical handling or compare alternative tabular backbones. Hyperparameter and optimization details are minimal. The evaluation is primarily under simulated missingness rather than a detailed analysis of MAR or MNAR. Conceptually, deterministic imputation also reduces sample diversity. The paper presents this as a feature when one wants a fast, stable, reproducible point imputation, but it acknowledges the corresponding drawback when uncertainty quantification or multiple imputation is required. The stochasticity ablation reflects that trade-off: introducing noise can sometimes slightly improve RMSE at large $$q(\mathbf{x}_t \mid \mathbf{x}_{t-1}) = \mathcal{N}(\mathbf{x}_t; \sqrt{1-\beta_t}\,\mathbf{x}_{t-1}, \beta_t \mathbf{I}),$$7, but at the expense of higher output variance (Zhou et al., 5 Aug 2025).